4.3
70 ratings
24 reviews

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 31 hours to complete

Suggested: 8 weeks of study, 6-8 hours per week...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 31 hours to complete

Suggested: 8 weeks of study, 6-8 hours per week...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
2 hours to complete

## Week 1: Introduction & Renewal processes

Upon completing this week, the learner will be able to understand the basic notions of probability theory, give a definition of a stochastic process; plot a trajectory and find finite-dimensional distributions for simple stochastic processes. Moreover, the learner will be able to apply Renewal Theory to marketing, both calculate the mathematical expectation of a countable process for any renewal process...
12 videos (Total 88 min), 1 quiz
12 videos
Week 1.1: Difference between deterministic and stochastic world4m
Week 1.2: Difference between various fields of stochastics6m
Week 1.3: Probability space8m
Week 1.4: Definition of a stochastic function. Types of stochastic functions.4m
Week 1.5: Trajectories and finite-dimensional distributions5m
Week 1.6: Renewal process. Counting process7m
Week 1.7: Convolution11m
Week 1.8: Laplace transform. Calculation of an expectation of a counting process-17m
Week 1.9: Laplace transform. Calculation of an expectation of a counting process-26m
Week 1.10: Laplace transform. Calculation of an expectation of a counting process-38m
Week 1.11: Limit theorems for renewal processes14m
1 practice exercise
Introduction & Renewal processes12m
Week
2
2 hours to complete

## Week 2: Poisson Processes

Upon completing this week, the learner will be able to understand the definitions and main properties of Poisson processes of different types and apply these processes to various real-life tasks, for instance, to model customer activity in marketing and to model aggregated claim sizes in insurance; understand a relation of this kind of models to Queueing Theory...
17 videos (Total 89 min), 1 quiz
17 videos
Week 2.2: Definition of a Poisson process as a special example of renewal process. Exact forms of the distributions of the renewal process and the counting process-23m
Week 2.3: Definition of a Poisson process as a special example of renewal process. Exact forms of the distributions of the renewal process and the counting process-34m
Week 2.4: Definition of a Poisson process as a special example of renewal process. Exact forms of the distributions of the renewal process and the counting process-44m
Week 2.5: Memoryless property5m
Week 2.6: Other definitions of Poisson processes-13m
Week 2.7: Other definitions of Poisson processes-24m
Week 2.8: Non-homogeneous Poisson processes-14m
Week 2.9: Non-homogeneous Poisson processes-24m
Week 2.10: Relation between renewal theory and non-homogeneous Poisson processes-14m
Week 2.11: Relation between renewal theory and non-homogeneous Poisson processes-27m
Week 2.12: Relation between renewal theory and non-homogeneous Poisson processes-34m
Week 2.13: Elements of the queueing theory. M/G/k systems-19m
Week 2.14: Elements of the queueing theory. M/G/k systems-25m
Week 2.15: Compound Poisson processes-16m
Week 2.16: Compound Poisson processes-26m
Week 2.17: Compound Poisson processes-33m
1 practice exercise
Poisson processes & Queueing theory14m
Week
3
1 hour to complete

## Week 3: Markov Chains

Upon completing this week, the learner will be able to identify whether the process is a Markov chain and characterize it; classify the states of a Markov chain and apply ergodic theorem for finding limiting distributions on states...
7 videos (Total 73 min), 1 quiz
7 videos
Week 3.2: Matrix representation of a Markov chain. Transition matrix. Chapman-Kolmogorov equation11m
Week 3.3: Graphic representation. Classification of states-110m
Week 3.4: Graphic representation. Classification of states-24m
Week 3.5: Graphic representation. Classification of states-37m
Week 3.6: Ergodic chains. Ergodic theorem-16m
Week 3.7: Ergodic chains. Ergodic theorem-215m
1 practice exercise
Markov Chains12m
Week
4
2 hours to complete

## Week 4: Gaussian Processes

Upon completing this week, the learner will be able to understand the notions of Gaussian vector, Gaussian process and Brownian motion (Wiener process); define a Gaussian process by its mean and covariance function and apply the theoretical properties of Brownian motion for solving various tasks...
8 videos (Total 87 min), 1 quiz
8 videos
Week 4.2: Gaussian vector. Definition and main properties19m
Week 4.3: Connection between independence of normal random variables and absence of correlation13m
Week 4.4: Definition of a Gaussian process. Covariance function-15m
Week 4.5: Definition of a Gaussian process. Covariance function-210m
Week 4.6: Two definitions of a Brownian motion18m
Week 4.7: Modification of a process. Kolmogorov continuity theorem7m
Week 4.8: Main properties of Brownian motion6m
1 practice exercise
Gaussian processes12m
4.3
24 Reviews

## 50%

got a tangible career benefit from this course

### Top Reviews

By ZMDec 1st 2018

Well presented course. I enjoyed it and was challenged a great deal. Thank you.

## Instructor

Assistant Professor
Faculty of economic sciences, HSE

## About National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

• Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.